Abstract
Pseudorandom sequences with good correlation properties are widely used in communications and cryptography. The search of new sequences with two-level autocorrelation has been a very interesting problem for decades. In 2002, Gong and Golomb proposed the iterative decimation-Hadamard transform (DHT) which is an useful tool to study two-level autocorrelation sequences. They showed that for all odd n ≤ 17, using the second-order decimation-Hadamard transform, and starting with a single binary m-sequence, all known two-level autocorrelation sequences of period 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> - <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> which have no subfield factorization can be obtained. In this paper, we present a new class of ternary or quaternary sequences with two-level autocorrelation using the second-order decimation-Hadamard transform. The period of such sequences is 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> - <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> .
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